Remark 2.4 The concept of GAC with \(U\cap \sigma \)  controls introduced above only apparently coincides with the definition considered, e.g., in the survey papers [1]}, [2]}. In fact, in the previous literature the function \(\sigma \)  was supposed to be increasing, in order to prevent unbounded inputs around the target. On the contrary, in Definition REF  it may happen that \(\lim _{r\rightarrow 0^+}\sigma (r)=+\infty \) , thus allowing for controls with \(L^\infty \)  norm diverging to \(+\infty \)  as the trajectory approaches \(\mathcal {C}\) .

